 13.4.1: In Exercises 110, find the total differential.z 2x2y
 13.4.2: In Exercises 110, find the total differential.z x2y
 13.4.3: In Exercises 110, find the total differential. 1x2 y2
 13.4.4: In Exercises 110, find the total differential.
 13.4.5: In Exercises 110, find the total differential.
 13.4.6: In Exercises 110, find the total differential. 12ex2y2 ex2y
 13.4.7: In Exercises 110, find the total differential. ex sin y
 13.4.8: In Exercises 110, find the total differential.w ey cos x z2
 13.4.9: In Exercises 110, find the total differential.w 2z 2 sin yz 3y sin x
 13.4.10: In Exercises 110, find the total differential.w x2yz w 2z 2 sin yz
 13.4.11: In Exercises 1116, (a) evaluate and and calculate and (b) use the t...
 13.4.12: In Exercises 1116, (a) evaluate and and calculate and (b) use the t...
 13.4.13: In Exercises 1116, (a) evaluate and and calculate and (b) use the t...
 13.4.14: In Exercises 1116, (a) evaluate and and calculate and (b) use the t...
 13.4.15: In Exercises 1116, (a) evaluate and and calculate and (b) use the t...
 13.4.16: In Exercises 1116, (a) evaluate and and calculate and (b) use the t...
 13.4.17: In Exercises 1720, find and use the total differential to approxima...
 13.4.18: In Exercises 1720, find and use the total differential to approxima...
 13.4.19: In Exercises 1720, find and use the total differential to approxima...
 13.4.20: In Exercises 1720, find and use the total differential to approxima...
 13.4.21: Define the total differential of a function of two variables
 13.4.22: Describe the change in accuracy of as an approximation of as and in...
 13.4.23: What is meant by a linear approximation of at the point Px0, y0?
 13.4.24: When using differentials, what is meant by the terms propagated err...
 13.4.25: Area The area of the shaded rectangle in the figure is The possible...
 13.4.26: Volume The volume of the red right circular cylinder in the figure ...
 13.4.27: Numerical Analysis A right circular cone of height and radius is co...
 13.4.28: Numerical Analysis The height and radius of a right circular cone a...
 13.4.29: Modeling Data Per capita consumptions (in gallons) of different typ...
 13.4.30: Rectangular to Polar Coordinates A rectangular coordinate system is...
 13.4.31: Volume The radius and height of a right circular cylinder are measu...
 13.4.32: Area A triangle is measured and two adjacent sides are found to be ...
 13.4.33: Wind Chill The formula for wind chill (in degrees Fahrenheit) is gi...
 13.4.34: Acceleration The centripetal acceleration of a particle moving in a...
 13.4.35: Volume A trough is 16 feet long (see figure). Its cross sections ar...
 13.4.36: Sports A baseball player in center field is playing approximately 3...
 13.4.37: Power Electrical power is given by where is voltage and is resistan...
 13.4.38: Resistance The total resistance of two resistors connected in paral...
 13.4.39: Inductance The inductance (in microhenrys) of a straight nonmagneti...
 13.4.40: Pendulum The period of a pendulum of length is where is the acceler...
 13.4.41: In Exercises 4144, show that the function is differentiable by find...
 13.4.42: In Exercises 4144, show that the function is differentiable by find...
 13.4.43: In Exercises 4144, show that the function is differentiable by find...
 13.4.44: In Exercises 4144, show that the function is differentiable by find...
 13.4.45: In Exercises 45 and 46, use the function to show that and both exis...
 13.4.46: In Exercises 45 and 46, use the function to show that and both exis...
 13.4.47: Show that if is differentiable at then is differentiable at Use thi...
 13.4.48: Consider the function (a) Evaluate and (b) Use the results of part ...
Solutions for Chapter 13.4: Differentials
Full solutions for Calculus  9th Edition
ISBN: 9780547167022
Solutions for Chapter 13.4: Differentials
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus , edition: 9. This expansive textbook survival guide covers the following chapters and their solutions. Since 48 problems in chapter 13.4: Differentials have been answered, more than 64305 students have viewed full stepbystep solutions from this chapter. Calculus was written by and is associated to the ISBN: 9780547167022. Chapter 13.4: Differentials includes 48 full stepbystep solutions.

Base
See Exponential function, Logarithmic function, nth power of a.

Bounded above
A function is bounded above if there is a number B such that ƒ(x) ? B for all x in the domain of ƒ.

Cone
See Right circular cone.

Directrix of a parabola, ellipse, or hyperbola
A line used to determine the conic

Equilibrium price
See Equilibrium point.

Focal axis
The line through the focus and perpendicular to the directrix of a conic.

Halflife
The amount of time required for half of a radioactive substance to decay.

Logistic growth function
A model of population growth: ƒ1x2 = c 1 + a # bx or ƒ1x2 = c1 + aekx, where a, b, c, and k are positive with b < 1. c is the limit to growth

Multiplication principle of probability
If A and B are independent events, then P(A and B) = P(A) # P(B). If Adepends on B, then P(A and B) = P(AB) # P(B)

Number line graph of a linear inequality
The graph of the solutions of a linear inequality (in x) on a number line

Obtuse triangle
A triangle in which one angle is greater than 90°.

Oddeven identity
For a basic trigonometric function f, an identity relating f(x) to f(x).

Position vector of the point (a, b)
The vector <a,b>.

Quotient identities
tan ?= sin ?cos ?and cot ?= cos ? sin ?

Random numbers
Numbers that can be used by researchers to simulate randomness in scientific studies (they are usually obtained from lengthy tables of decimal digits that have been generated by verifiably random natural phenomena).

Relation
A set of ordered pairs of real numbers.

Shrink of factor c
A transformation of a graph obtained by multiplying all the xcoordinates (horizontal shrink) by the constant 1/c or all of the ycoordinates (vertical shrink) by the constant c, 0 < c < 1.

Solve by elimination or substitution
Methods for solving systems of linear equations.

Variable
A letter that represents an unspecified number.

Ymin
The yvalue of the bottom of the viewing window.